# Why symmetric rounding nets to zero

Across evenly spread totals the ups and downs cancel exactly. That is not a coincidence; it is why this rule was chosen.

**Net effect: $0.00 per thousand cash transactions. Essentially zero, which is what symmetric rounding is designed to do. There is no margin here to capture.**

| | |
| --- | --- |
| Rule | symmetric |
| Tax rate | 0% |
| Transactions | 100 |
| Mean delta per transaction | 0¢ |
| Per 1,000 cash sales | $0.00 |
| Rounded up / down / unchanged | 40 / 40 / 20 |

## Every price

| Price | Exact total | Due in cash | Delta |
| --- | --- | --- | --- |
| $0.01 | $0.01 | $0.00 | -1¢ |
| $0.02 | $0.02 | $0.00 | -2¢ |
| $0.03 | $0.03 | $0.05 | +2¢ |
| $0.04 | $0.04 | $0.05 | +1¢ |
| $0.05 | $0.05 | $0.05 | 0¢ |
| $0.06 | $0.06 | $0.05 | -1¢ |
| $0.07 | $0.07 | $0.05 | -2¢ |
| $0.08 | $0.08 | $0.10 | +2¢ |
| $0.09 | $0.09 | $0.10 | +1¢ |
| $0.10 | $0.10 | $0.10 | 0¢ |
| $0.11 | $0.11 | $0.10 | -1¢ |
| $0.12 | $0.12 | $0.10 | -2¢ |
| $0.13 | $0.13 | $0.15 | +2¢ |
| $0.14 | $0.14 | $0.15 | +1¢ |
| $0.15 | $0.15 | $0.15 | 0¢ |
| $0.16 | $0.16 | $0.15 | -1¢ |
| $0.17 | $0.17 | $0.15 | -2¢ |
| $0.18 | $0.18 | $0.20 | +2¢ |
| $0.19 | $0.19 | $0.20 | +1¢ |
| $0.20 | $0.20 | $0.20 | 0¢ |
| $0.21 | $0.21 | $0.20 | -1¢ |
| $0.22 | $0.22 | $0.20 | -2¢ |
| $0.23 | $0.23 | $0.25 | +2¢ |
| $0.24 | $0.24 | $0.25 | +1¢ |
| $0.25 | $0.25 | $0.25 | 0¢ |
| $0.26 | $0.26 | $0.25 | -1¢ |
| $0.27 | $0.27 | $0.25 | -2¢ |
| $0.28 | $0.28 | $0.30 | +2¢ |
| $0.29 | $0.29 | $0.30 | +1¢ |
| $0.30 | $0.30 | $0.30 | 0¢ |
| $0.31 | $0.31 | $0.30 | -1¢ |
| $0.32 | $0.32 | $0.30 | -2¢ |
| $0.33 | $0.33 | $0.35 | +2¢ |
| $0.34 | $0.34 | $0.35 | +1¢ |
| $0.35 | $0.35 | $0.35 | 0¢ |
| $0.36 | $0.36 | $0.35 | -1¢ |
| $0.37 | $0.37 | $0.35 | -2¢ |
| $0.38 | $0.38 | $0.40 | +2¢ |
| $0.39 | $0.39 | $0.40 | +1¢ |
| $0.40 | $0.40 | $0.40 | 0¢ |

Showing the first 40 of 100; the totals above cover all.

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